8.2.2.4 Output Capacitor

There are three primary considerations for selecting the value of the output capacitor. The output capacitor determines the modulator pole, the output voltage ripple, and how the regulator responds to a large change in load current. The output capacitance needs to be selected based on the most stringent of these three criteria.

The desired response to a large change in the load current is the first criteria. The output capacitor needs to supply the increased load current until the regulator responds to the load step. The regulator does not respond immediately to a large, fast increase in the load current such as transitioning from no load to a full load. The regulator usually needs two or more clock cycles for the control loop to sense the change in output voltage and adjust the peak switch current in response to the higher load. The output capacitance must be large enough to supply the difference in current for 2 clock cycles to maintain the output voltage within the specified range. Equation 32 shows the minimum output capacitance necessary, where ΔI_OUT is the change in output current, ƒsw is the regulators switching frequency and ΔV_OUT is the allowable change in the output voltage. For this example, the transient load response is specified as a 4% change in V_OUT for a load step from 0.875 A to 2.625 A. Therefore, ΔI_OUT is 2.625 A – 0.875 A = 1.75 A and ΔV_OUT = 0.04 × 3.3 = 0.13 V. Using these numbers gives a minimum capacitance of 44.9 μF. This value does not take the ESR of the output capacitor into account in the output voltage change. For ceramic capacitors, the ESR is usually small enough to be ignored. Aluminum electrolytic and tantalum capacitors have higher ESR that must be included in load step calculations.

The output capacitor must also be sized to absorb energy stored in the inductor when transitioning from a high to low load current. The catch diode of the regulator can not sink current so energy stored in the inductor can produce an output voltage overshoot when the load current rapidly decreases. A typical load step response is shown in Figure Figure 33. The excess energy absorbed in the output capacitor will increase the voltage on the capacitor. The capacitor must be sized to maintain the desired output voltage during these transient periods. Equation 33 calculates the minimum capacitance required to keep the output voltage overshoot to a desired value, where L_O is the value of the inductor, I_OH is the output current under heavy load, I_OL is the output under light load, V_f is the peak output voltage, and V_I is the initial voltage. For this example, the worst case load step will be from 2.625 A to 0.875 A. The output voltage increases during this load transition and the stated maximum in our specification is 4 % of the output voltage. This makes V_f = 1.04 × 3.3 = 3.432. Vi is the initial capacitor voltage which is the nominal output voltage of 3.3 V. Using these numbers in Equation 33 yields a minimum capacitance of 38.6 μF.

Equation 34 calculates the minimum output capacitance needed to meet the output voltage ripple specification, where ƒsw is the switching frequency, V_ORIPPLE is the maximum allowable output voltage ripple, and I_RIPPLE is the inductor ripple current. Equation 34 yields 11.4 μF.

Equation 35 calculates the maximum ESR an output capacitor can have to meet the output voltage ripple specification. Equation 35 indicates the ESR should be less than 18 mΩ.

The most stringent criteria for the output capacitor is 44.9 μF required to maintain the output voltage within regulation tolerance during a load transient.

Capacitance de-ratings for aging, temperature and DC bias increases this minimum value. For this example, 100-μF ceramic capacitors with 5 mΩ of ESR is used. The derated capacitance is 70 µF, well above the minimum required capacitance of 44.9 µF.

Capacitors are generally rated for a maximum ripple current that can be filtered without degrading capacitor reliability. Some capacitor data sheets specify the root mean square (RMS) value of the maximum ripple current. Equation 36 can be used to calculate the RMS ripple current that the output capacitor must support. For this example, Equation 36 yields 261 mA.

Equation 32.

Equation 33.

Equation 34.

Equation 35.

Equation 36.